Taking possession of the gift

Q: Zaid, Umar, and Bakr are friends. Zaid has an item in his hand and asks Umar, "Umar, do you want this?" Umar replies in the affirmative. Zaid then places the item on the table in front of him. Umar leaves the room without the item. He intends fetching the item later on. Bakr is not aware of all this. Later in the day, Umar sees Bakr going home with the same item. When Umar asks Zaid about this, Zaid replies: "You did not take physical possession of the item. I thought you never want this gift. That is why I gave it to Bakr." Umar objects saying that he responded in the affirmative when Zaid asked if he wanted the item.

1. Who truly owns the item?

2. Is it true that since Umar did not take physical possession of the item, it still belongs to the original owner, Zaid?

Changing one's niyyat before the fast commences

Q: I made a niyyat for a nafil fast about 30min before sehri ends. Just prior to sehri ending, I decided that I should rather wait and make the niyyat for keeping fast before half the day, depending on how I felt. I was not going to eat during that time, until my niyyat was confirmed. Is it ok to change my niyyat for fasting afterwards, or is the first niyyat I made 30 minutes before sehri ended binding?